(for \(i,j\)  in the ranges listed above)
and the components of the moment map \(\mu \)  are (see [1]}, Equation (39))
\(  \mu _j (a,\, b,\, u\,, v)\, = \,(v_j)^{-1} ~~~ (j \,= \,1,\, \dots ,\, r)\) 
\( \mu _0(a,\, b,\, u,\, v) \,= \,{\rm Ad}_{u_1} (v_1)\cdots {\rm Ad}_{u_r} (v_r) [a_1,\, b_1] \cdots [a_g,\, b_g].\) 
